Atoms and Molecules. 909 



intersect at an eccentricity about - 82. For all eccentricities 

 less than this the unknown radius, a, would have to be 

 greater than the semi-major axis of the ellipse, when the 

 equivalent ring would lie wholly outside of the ellipsoid, 

 a result that is physically absurd. The eccentricity must 

 certainly be greater than '82 in order to satisfy (26) and 

 reduce the r~ 6 coefficient to zero, and must lie between '82 

 and unity as an upper limit. At an eccentricity *9 it is 

 seen that a/b=l'57, a /6=--2'3, and a/a = *68. A rough 

 estimation of the position of the equivalent radius would 

 indicate that '9 is certainly a lower limit for the eccentricity. 

 There is no obvious way to compute the radius a from electro- 

 static forces alone. 



It seems, therefore, remarkable that the eccentricity of 

 the electron as determined in the first paper * by an entirely 

 different method should have yielded a value within the 

 limits above found, namely e=*945, corresponding to ratios 

 a/,6 = l'5, a/a = 'D approximately, and a /b = 3*058, shown in 

 fig. 6 by the ordinate at '945. These two independent 

 determinations taken together not only help to establish the 

 non-spherical form of the electron, but they approximately 

 determine its value within fairly narrow limits. 



Let us now proceed with the assumption that (29) is 

 exactly satisfied by the properties of the electron, and 

 examine the values that the various coefficients assume 

 by introducing this relation. From (2Q) we have 



pa 2 == 2b\ p 2 a± = 46*, 



pa* = 4&/p, p 2 a 6 = 8¥/p, 



pa 6 = 8b*/p 2 , p 2 a 8 = Ub 8 /p 2 , 



pa' =■ 16b*lp\ . . . (30) 



and these values reduce both (E + C) and (Gr + E') in (25) 

 to zero identically. That is to say, both the r~ & and the 

 r~ 8 terms of the series disappear together, while the co- 

 efficient of the r~ 10 term, (I + G 7 ), becomes 



(__31500 + 18900/p-2835/|O 2 )/A . . . (31) 



Using the value of the eccentricity as first determined, 

 namely '945, p is given by (28), and ljp is 1*12 approxi- 

 mately. Hence the whole electrostatic force between the 

 two atoms given by (25) becomes numerically 



F = ^(-27776/A- 10 ...), . . . (32) 



atom ABC * 



on atom abc. 



* Phil. Mag. Oct. 1921, equation (76). 



